Robust parameter estimation for rational ordinary differential equations

Oren Bassik, Yosef Berman, Soo Go, Hoon Hong, Ilia Ilmer, Alexey Ovchinnikov, Chris Rackauckas, Pedro Soto and Chee Yap

Applied Mathematics and Computation, 2026, vol. 509, issue C

Abstract: We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a loop, the corresponding outputs are computed by solving the ODE numerically, followed by computing the error from the given time series data. If the error is small, the loop terminates and the parameter values are returned. Otherwise, heuristics/theories are used to possibly improve the guess and continue the loop. These approaches tend to be non-robust in the sense that their accuracy often depends on the search interval and the true parameter values; furthermore, they cannot handle cases where the parameters are only locally identifiable.

Keywords: Parametric ODE models; Parameter estimation; Differential algebra; Symbolic-numeric differentiation; Mathematical software (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:509:y:2026:i:c:s0096300325003649

DOI: 10.1016/j.amc.2025.129638

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